How does Merge Sort operate on an array?

Merge Sort operates by dividing the array into halves and then merging those halves back together in a sorted order. It follows a divide-and-conquer strategy, which is key to its efficiency.

Initially, Merge Sort splits the array into two equal halves. This division continues recursively until each sub-array contains a single element, as a single-element array is trivially sorted. Once the array is divided down to these single-element arrays, the algorithm begins merging these smaller arrays back together. During this merge process, it compares the individual elements of the smaller arrays, combining them into larger arrays in a sorted manner.

The merging step is crucial, as it ensures that the resulting arrays are sorted at each level of the recursion. This process continues until the entire array is merged back together into a fully sorted array. The systematic division and merging ensure that Merge Sort maintains an average time complexity of O(n log n), making it efficient for larger datasets.

This rationale highlights why the method of dividing the array into halves and merging them together is the essence of how Merge Sort functions, distinguishing it from other sorting algorithms that employ different strategies, such as quicksort or tree-based algorithms.